object separating itself during softbody simulation
That is a tricky problem.
The mesh geometry (length of the edges for instance) is of influence on the physics settings (like Edges Push and Pull values) and thus on how the object behaves during physics simulation. Because you have essentially two (very different) meshes in one object, they behave differently.
You could try to simply connect the to meshes in Edit Mode:

But the added edges will somewhat influence the shape of your meshes:

Also I don't think it will work for your jellyfish, since it is a more complicated mesh. I think if you want to control the behavior of both meshes, you'll have to make them two different objects, and sync their movement. I think I would animate the jellyfish manually without physics, to follow the movement of the ball.
(You might not need it, but just in case: If you were to do this, it might help to know about Cache setting to keep you simulation from changing for some reason. Can I save the baking cache?)
Not great answer I think, but I hope it helps. : )